SOLVE THE FOLLOWING INEQUALITIES: X2 2X 15 6X2 X 2 12X2 3 13X 4X2 2X 3 0

1. x +2x<15 solution: x +2x-15<0 x-3)(x+2)<0 when x 3, x-3 0, x+2>0, no solution; When x -2, x-3<0, x+2 0, no solution; When -20, x-3)(x+2)<0. So, the solution of the original inequality is.

23-13x solution: -12x +13x-3>0, 12x -13x+3<0, (4x-3)(3x-1)<0, the solution of the original inequality is 1 30, (x-3 2 4)(x+ 2 2)>0, the solution of the original inequality is.

x>3 2 4 or x<-2 2

x²+3x+10=0

x²-3x-10=0

x-5)(x+2)=0

x1=5 x2=-2

2x²-3x-1=0

b²-4ac=9+8=17

Substituting the root-seeking formula.

x=(3±√17)/4

x1=(3+ 17) 4 x2=(3- Stove pants spring 17) 4x(x-1) (x-2)(x+3).

x²-x>x²+x-6

6>x+x

2x,1, the solution is resistant to the following equations or inequalities: -x pure Kai +3x+10=0 2x -3x-1=0 x(x-1) (x-2)(x+3) -x +3x-1 -5

Method 1: Quadratic curve analysis:

Quadratic curves. y

2-x)(3-x)

x-2)(x-3)

x 25x6, is a parabola, with the opening pointing upwards, and the intersection points with the x-axis are (2,0) and (3,0), and the middle part of the two intersection points is y<0, so that when 2

0, or (2).

2-x>0 and 3-x<0.

Consider the possibility (1): 2-x

x3-xx The above two conditions must be met at the same time, so 2

It is not possible that the above two conditions must be met at the same time for x3-xx.

Solution: 3x-2(9-x)>3(7+2x)-(11-6x) are obtained from the original formula.

3x-18+2x>21+6x-11+6x, i.e. 5x-18>10+12x

28>7x

Solution x 4

2(3x-1)-3(4x+5) x-4(x-7) is obtained from the original formula.

6x-2-12x-15 x-4x+28, i.e. -6x-17 -3x+28

45 3x solution x -15

So, the solution set for the group of inequalities is {x -15 x -4

1) The numerator and denominator are multiplied by -1, and the inequality does not change: (x 22x-3) (2x 2-4x

5) "Qi Ru imitates the denominator of Oak Town. 2x^2-4x

5=(2x^2-4x

3=2(x^2-2x

3=2(x-1)^2

3》3> The denominator is positive, and the denominator does not change. 2x^2-4x5>x^2

2x-3。(2x^2-x^2)-4x-2x3)>

8=(x-2)(x-4)>0。The zero point is obviously , x<2 or x> high fiber 4.

This is a group of inequalities: -4x 2+4x -3

Moreover. -4x 2+4x 0, respectively, -1 2 x 3 2, and. x 0 or.

x 1 combined. -1/2＜x≤0

Or. 1≤x＜3/2

1. Divide both sides of the unequal sign by 2 at the same time to obtain: -x<7

2. Multiply -1 on both sides of the unequal sign at the same time, (the unequal sign changes direction) to get x>-7

Answer: Divide it into two inequalities to form.

Inequality groups. to answer:

2x－1<4x+13<4x-5

That is: 2x-1<4x+13

4x+13<4x-5

So: -1-13<4x-2x

4x-4x<-5-13

That is: 2x>-14, x>-7

0<-18 is not established.

So: there is no solution to the group of inequalities.

1) 3x 2-x-4>0

3x-4)(x+1)﹥0

x 4 3 or the first old x -1

2)x^2-x-12